You are required to design a binary clock using a binary counting system to display time by addressing each segment (hours, minutes, and seconds) with its own byte. Each byte is broken into two parts, the first half representing the tens place and the second showing the ones place of a particular number. For example, if the byte representing hours shows 010010 that equates out to 12 hours. You have been asked to make a binary clock using a matrix of LEDs and a control system that can continue to monitor time while continuing to update its outputs. By creating a matrix of LEDs, you will be able to control a higher number of LEDs with the same number of digital output lines. In this two-part module you may build an 8-bit binary clock that displays individual characters at a time. You may then design and build an LED matrix that will be driven by NPN transistors. That is capable of displaying multiple characters.

Memory addresses are required to be displayed as two hex numbers. An example is C800:5. The part to the left of the colon (C800) is called the segment address, and the part to the right of the colon (5) is called the offset. The offset value can have as many as four hex digits. The actual memory address is calculated by adding a zero to the right of the segment address and adding the offset value, like this: C800:5 = C8000 + 5 = C8005.

C8005 is called as the absolute or linear address of the memory. Similarly, F000: FFFD can be computed to get the memory address.

You are also required to find the memory address in F000: FFFD in Binary and Decimal.

Task Part 1

A linear shock absorber model was used to study the peak amplitude of vibration of the sprung mass of the car as a result of two components of displacements as follows:

() = 6sin(1200+65) 4sin(1200+46)

Here, the phase angles are given in degrees. You are supposed to obtain the peak amplitude of () as well as its phase angle exclusively using complex number theories. You may also plot () as the sum of its 2 components and its 2 components on the same graph to verify the answer.

Shock absorber non-linear model produced a displacement profile which has a fundamental component of the frequency of 0.4 rad/s superimposed with a 5th order harmonic component of the frequency of 2.0 rad/s as follows:

()=2sin0.4+1.4sin2 cm

where is in seconds. You are faced with a situation where there is no access to advanced analytical software but only a scientific calculator. To that end, you are compelled to use De Moivres theorem to express () as a function of

sin0.4 ()=2sin0.4+1.4 sin2=(sin0.4)

and hence use root-finding techniques of polynomial functions to find the time instances where ()=0. In order to accomplish this, you may first check the correctness of the trigonometric identity sin5=16sin520sin3+5sin. Later on, you are also asked to use commercially available software to plot () versus to verify the answers of ()=0 as well as the peak amplitude of ().